Yes but not the way I think you are thinking. The closing costs are added to the basis and depreciated as part of the unit's price. So the first 3 begin depreciation in 2020 for 27.5 years while your unit begins in 2021 for 27.5 years.
You have a 4 plex. Are you counting this as a 3 unit item A for 2020 and then your unit as item B in 2021? Or are you counting each unit on its own? If you decide to sell one unit, it is easier when they are separated. If you will only sell as a group, then just the two rental parts. It is not and can't be one unit.
This article, Topic No. 414 Rental Income and Expenses, has lots of great links and information to help you along your rental journey.
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